Quantum Monte Carlo Simulation of the 3D Ising Transition on the Fuzzy Sphere

Abstract

We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional $SU(2)$ layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.

12 pages, 7 figures

References in corpus (4)

• Uncovering conformal symmetry in the $3D$ Ising transition: State-operator correspondence from a fuzzy sphere regularization
• Landau Level Quantization on the Sphere
• Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Sphere
• 3D Ising CFT and Exact Diagonalization on Icosahedron: The Power of Conformal Perturbation Theory

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• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• A Fuzzy Sphere Journey in Critical Phenomena
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere